Question

Prove that (1-cosA) (1-secA) = tanA SinA

Answer 1

There is a mistake in the given problem: It should be (1 - cos A) (1 + sec A).

(1 - cosA) (1 + secA)
   = 1 - cosA + secA - cos A sec A
   = 1 - cos A + 1/cos A - 1
   =  ( 1 - cos ² A) / cos A
   = sin² A / cos A
   = sin A  *  sin A /cos A
   = sin A * tan A

Answer 2

Answer:-

(sin^2A / cosA = I (sinA)^2 * secA

= (1-cos ^2A) sec A

= ( 1- cosA) * ( 1+ cosA) sec A

= ( 1-cosA) ( secA + secA coA)

= ( 1-cosA) ( secA + 1)